Author 
Message 
TAGS:

Hide Tags

Director
Status: I don't stop when I'm Tired,I stop when I'm done
Joined: 11 May 2014
Posts: 563
Location: Bangladesh
Concentration: Finance, Leadership
GPA: 2.81
WE: Business Development (Real Estate)

The symbol ∆ denotes one of the four arithmetic operations:addition,su [#permalink]
Show Tags
22 Jun 2017, 15:18
6
This post received KUDOS
2
This post was BOOKMARKED
Question Stats:
66% (00:52) correct 34% (00:46) wrong based on 454 sessions
HideShow timer Statistics
The symbol ∆ denotes one of the four arithmetic operations:addition,subtraction,multiplication,or division,If 6∆3≤ 3 ,which of the following must be true ? I. 2∆2 = 0 II. 2∆2 = 1 III. 4∆2 = 2 A. I only B. II only C. III only D. I and II only E. I, II, and III
Official Answer and Stats are available only to registered users. Register/ Login.
_________________
Md. Abdur Rakib
Please Press +1 Kudos,If it helps Sentence CorrectionCollection of Ron Purewal's "elliptical construction/analogies" for SC Challenges



VP
Joined: 22 May 2016
Posts: 1342

Re: The symbol ∆ denotes one of the four arithmetic operations:addition,su [#permalink]
Show Tags
22 Jun 2017, 16:43
1
This post received KUDOS
1
This post was BOOKMARKED
AbdurRakib wrote: The symbol ∆ denotes one of the four arithmetic operations: addition,subtraction,multiplication,or division. If 6∆3≤ 3, which of the following must be true ?
I.2∆2=0 II.2∆2=1 III.4∆2=2
A. I only B. II only C. III only D. I and II only E. I, II, and III If 6 ∆ 3 ≤ 3, the ∆ operator is subtraction AND division. 6  3 = 3, which satisfies the equation \(\frac{6}{3}\) = 2, which also satisfies the equation (2 is less than 3). The operator cannot be addition or multiplication. 6 + 3 = 9, which is > 3. And 6 * 3 = 18, also > than 3. Check I, II, and III. I. 2 ∆ 2 = 0. If ∆ were only subtraction, this would be fine. 2  2 = 0. But \(\frac{2}{2}\) = 1. This equation is not true when ∆ is division. Incorrect. II. 2 ∆ 2 = 1. If ∆ were only division, this would be fine.\(\frac{2}{2}\) = 1. But from above, 2  2 = 0. This equation does not holds true when ∆ is subtraction. Incorrect. III. 4 ∆ 2 = 2. This must be true for both subtraction and division. It holds for subtraction. 4  4 = 2. And it holds for division: \(\frac{4}{2}\)= 2. Correct. Answer C
_________________
At the still point, there the dance is.  T.S. Eliot Formerly genxer123
Last edited by generis on 22 Jun 2017, 16:58, edited 2 times in total.



Director
Joined: 04 Dec 2015
Posts: 696
Location: India
Concentration: Technology, Strategy
WE: Information Technology (Consulting)

Re: The symbol ∆ denotes one of the four arithmetic operations:addition,su [#permalink]
Show Tags
22 Jun 2017, 16:49
1
This post was BOOKMARKED
AbdurRakib wrote: The symbol ∆ denotes one of the four arithmetic operations:addition,subtraction,multiplication,or division,If 6∆3≤ 3 ,which of the following must be true ?
I.2∆2=0 I I .2∆2=1 I I I .4∆2=2
A. I only B. II only C. III only D. I and II only E. I, II, and III \(6∆3≤ 3\)
\(\frac{6}{3}= 3\)
\(63 = 3\)
Therefore symbol ∆ should be division and subtraction both.
Checking the options, we get;
I.\(2∆2=0\)
\(2  2 = 0\)
\(\frac{2}{2}= 1\) Must Not be true.
II .\(2∆2=1\)
\(\frac{2}{2}= 1\)
\(2  2 = 0\)  Must Not be true.
III .\(4∆2=2\)
\(\frac{4}{2} = 2\)  Must be true.
\(4  2 = 2\)  Must be true.
Hence Only III must be true. Answer (C)...



Senior Manager
Joined: 28 May 2017
Posts: 296
Concentration: Finance, General Management

Re: The symbol ∆ denotes one of the four arithmetic operations:addition,su [#permalink]
Show Tags
23 Jun 2017, 00:59
AbdurRakib wrote: The symbol ∆ denotes one of the four arithmetic operations:addition,subtraction,multiplication,or division,If 6∆3≤ 3 ,which of the following must be true ?
I.2∆2=0 I I .2∆2=1 I I I .4∆2=2
A. I only B. II only C. III only D. I and II only E. I, II, and III ∆ could be either Subtraction or Division in order to fulfill condition 6∆3≤ 3 I  2∆2=0  In this condition, ∆ denotes only subtraction and not Division. Hence Wrong II  2∆2=1  In this condition, ∆ denotes only Division and not subtraction. Hence Wrong III  4∆2=1  In this condition, ∆ denotes either Division or subtraction. Hence Correct. hence, Answer C
_________________
If you like the post, show appreciation by pressing Kudos button



Manager
Joined: 17 Feb 2016
Posts: 106
Location: India
Concentration: General Management, Entrepreneurship
GPA: 3.12
WE: Education (Internet and New Media)

Re: The symbol ∆ denotes one of the four arithmetic operations:addition,su [#permalink]
Show Tags
23 Jun 2017, 01:24
From the context, \(∆= subtraction and division\) ∆= subtraction\(63<=3\) ∆= division\(\frac{6}{3}=2<=3\) From the options Only iii holds true as 4∆2=2( both division and subtraction) Option c
_________________
Never stop fighting until you arrive at your destined place  that is, the unique you. Have an aim in life, continuously acquire knowledge, work hard, and have the perseverance to realise the great life. A. P. J. Abdul Kalam



Target Test Prep Representative
Status: Head GMAT Instructor
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2001

Re: The symbol ∆ denotes one of the four arithmetic operations:addition,su [#permalink]
Show Tags
26 Jun 2017, 17:00
AbdurRakib wrote: The symbol ∆ denotes one of the four arithmetic operations:addition,subtraction,multiplication,or division,If 6∆3≤ 3 ,which of the following must be true ?
I.2∆2=0 I I .2∆2=1 I I I .4∆2=2
A. I only B. II only C. III only D. I and II only E. I, II, and III Let’s analyze the given inequality: If ∆ = addition: 6 + 3 ≤ 3 9 ≤ 3 Since 9 is not less than 3, ∆ cannot be addition. If ∆ = subtraction: 6  3 ≤ 3 3 ≤ 3 Since 3 is less than or equal to 3, ∆ can be subtraction. If ∆ = divison: 6/3 ≤ 3 2 ≤ 3 Since 2 is less than or equal to 3, ∆ can be division. If ∆ = multiplication: 6 x 3 ≤ 3 18 ≤ 3 Since 18 is not less than or equal to 3, ∆ cannot be multiplication. We see then that ∆ is either subtraction or division. Now let’s analyze each Roman numeral: I. 2∆2=0 Since 2/2 does not equal 0, division doesn’t work and I is not true. II. 2∆2=1 Since 2  2 does not equal 1, subtraction doesn’t work and II is not true. III. 4∆2=2 Since 4  2 = 2 and 4/2 = 2, III is true. Answer: C
_________________
Jeffery Miller
Head of GMAT Instruction
GMAT Quant SelfStudy Course
500+ lessons 3000+ practice problems 800+ HD solutions



SVP
Joined: 11 Sep 2015
Posts: 2055
Location: Canada

Re: The symbol ∆ denotes one of the four arithmetic operations:addition,su [#permalink]
Show Tags
27 Jun 2017, 14:49
AbdurRakib wrote: The symbol ∆ denotes one of the four arithmetic operations:addition,subtraction,multiplication,or division,If 6∆3≤ 3 ,which of the following must be true ?
I. 2∆2=0 II. 2∆2=1 III. 4∆2=2
A. I only B. II only C. III only D. I and II only E. I, II, and III The above solutions are perfect. I just want to point out that, when answering this type of question type (where the answer choices are I only, II and III only, etc.), be sure to ELIMINATE answer choices after examining each statement. So, for example, once we determine that statement I need not be true, we can ELIMINATE answer choices A, D and E Then, once we determine that statement II need not be true, we can ELIMINATE answer choice B At this point, there's no need to check statement III, since we already know that the correct answer must be C Cheers, Brent
_________________
Brent Hanneson – Founder of gmatprepnow.com



Intern
Joined: 16 Feb 2016
Posts: 25

Re: The symbol ∆ denotes one of the four arithmetic operations:addition,su [#permalink]
Show Tags
10 Jul 2017, 11:43
1
This post received KUDOS
AbdurRakib wrote: The symbol ∆ denotes one of the four arithmetic operations:addition,subtraction,multiplication,or division,If 6∆3≤ 3 ,which of the following must be true ?
I.2∆2=0 I I .2∆2=1 I I I .4∆2=2
A. I only B. II only C. III only D. I and II only E. I, II, and III I read the options as III (.4)∆2=2 and got it all wrong!! That dot, right after the Roman Numerals, is so confusing...! The dot is closer to the digit, rather, it should be closer to the Roman numeral, to avoid any confusion! So I suggest, this question must be edited! Thanks, ashygoyal



Math Expert
Joined: 02 Sep 2009
Posts: 43866

Re: The symbol ∆ denotes one of the four arithmetic operations:addition,su [#permalink]
Show Tags
10 Jul 2017, 11:48
ashygoyal wrote: AbdurRakib wrote: The symbol ∆ denotes one of the four arithmetic operations:addition,subtraction,multiplication,or division,If 6∆3≤ 3 ,which of the following must be true ?
I.2∆2=0 I I .2∆2=1 I I I .4∆2=2
A. I only B. II only C. III only D. I and II only E. I, II, and III I read the options as III (.4)∆2=2 and got it all wrong!! That dot, right after the Roman Numerals, is so confusing...! The dot is closer to the digit, rather, it should be closer to the Roman numeral, to avoid any confusion! So I suggest, this question must be edited! Thanks, ashygoyal Edited as suggested. Thank you.
_________________
New to the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
Collection of Questions: PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics



Director
Joined: 13 Mar 2017
Posts: 563
Location: India
Concentration: General Management, Entrepreneurship
GPA: 3.8
WE: Engineering (Energy and Utilities)

Re: The symbol ∆ denotes one of the four arithmetic operations:addition,su [#permalink]
Show Tags
10 Jul 2017, 22:21
1
This post received KUDOS
AbdurRakib wrote: The symbol ∆ denotes one of the four arithmetic operations:addition,subtraction,multiplication,or division,If 6∆3≤ 3 ,which of the following must be true ?
I. 2∆2 = 0 II. 2∆2 = 1 III. 4∆2 = 2
A. I only B. II only C. III only D. I and II only E. I, II, and III 6∆3≤ 3 So, 6  3 = 3 6/3 = 2 I. 2∆2 22 = 0 2/2 = 1 So it may be true. II. 2∆2 22 = 0 2/2 = 1 So it is may be true. III. 4∆2 42 = 2 4/2 = 2 So, 4∆2 = 2 must be true. Answer C.
_________________
CAT 99th percentiler : VA 97.27  DILR 96.84  QA 98.04  OA 98.95
MBA Social Network : WebMaggu
Appreciate by Clicking +1 Kudos ( Lets be more generous friends.)



Verbal Forum Moderator
Status: Greatness begins beyond your comfort zone
Joined: 08 Dec 2013
Posts: 1912
Location: India
Concentration: General Management, Strategy
GPA: 3.2
WE: Information Technology (Consulting)

Re: The symbol ∆ denotes one of the four arithmetic operations:addition,su [#permalink]
Show Tags
11 Jul 2017, 00:06
AbdurRakib wrote: The symbol ∆ denotes one of the four arithmetic operations:addition,subtraction,multiplication,or division,If 6∆3≤ 3 ,which of the following must be true ?
I. 2∆2 = 0 II. 2∆2 = 1 III. 4∆2 = 2
A. I only B. II only C. III only D. I and II only E. I, II, and III 6∆3≤ 3 ∆ can denote subtraction or division . 6+3=9 and 9> 3 6*3 = 18 and 18 >3 I. 2∆2 = 0 , If ∆ is division , then the expression is invalid II. 2∆2 = 1 , If ∆ is subtraction , then the expression is invalid III. 4∆2 = 2  Correct Answer C
_________________
When everything seems to be going against you, remember that the airplane takes off against the wind, not with it.  Henry Ford The Moment You Think About Giving Up, Think Of The Reason Why You Held On So Long +1 Kudos if you find this post helpful



Intern
Joined: 27 Dec 2016
Posts: 15

Re: The symbol ∆ denotes one of the four arithmetic operations:addition,su [#permalink]
Show Tags
21 Aug 2017, 21:40
1
This post received KUDOS
Thinking that even one criteria satisfies the condition, I have interpreted that all three options are valid
Since the question says 6∆3=<3 6/3 = 2 63 = 3 I applied the conditions individually for all three and opted for E. But didn't strike that one of the option should satisfy both conditions.



EMPOWERgmat Instructor
Status: GMAT Assassin/CoFounder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 11059
Location: United States (CA)
GRE 1: 340 Q170 V170

Re: The symbol ∆ denotes one of the four arithmetic operations:addition,su [#permalink]
Show Tags
09 Jan 2018, 17:39
Hi All, We're told that the symbol # denotes one of the four arithmetic operations: addition, subtraction, multiplication, or division and that 6#3 <= 3. We're asked which of the three Roman Numerals must be true. To start, let's do a bit of analysis on the inequality that we're given (and determine which math operation COULD fit this): 6#3 <= 3 6 + 3 = 9 which is NOT <= 3 6  3 = 3 which IS <= 3 (6)(3) = 18 which is NOT <= 3 6/3 = 2 which IS <=3 Thus, the symbol # must be either subtraction or division (although we don't know which one for sure). I. 2#2 = 0 We've proven that the symbol is either subtraction or division, so let's see if either of those operations 'fits' this information... 2  2 = 0 2/2 = 1 Thus, if the symbol is subtraction, then Roman Numeral 1 IS true. However, if the symbol is division, then Roman Numeral 1 is NOT true. There's no way to know which symbol is involved though, so Roman Numeral 1 is not necessarily true. Eliminate Answers A, D and E. II. 2#2 = 1 With the work that we've done in Roman Numeral 1 (above), we already know that the outcome of 2#2 could be 0 or 1. This inconsistency also provides that Roman Numeral 2 is not necessarily true. Eliminate Answer B. There's only one answer remaining.... III. 4#2 = 2 You can still prove that Roman Numeral 3 is always true... 4  2 = 2 4/2 = 2 Both outcomes 'fit' the information in Fact 3, so regardless of what operation is represented, the statement IS true. Final Answer: GMAT assassins aren't born, they're made, Rich
_________________
760+: Learn What GMAT Assassins Do to Score at the Highest Levels Contact Rich at: Rich.C@empowergmat.com
Rich Cohen
CoFounder & GMAT Assassin
Special Offer: Save $75 + GMAT Club Tests Free
Official GMAT Exam Packs + 70 Pt. Improvement Guarantee www.empowergmat.com/
***********************Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!***********************




Re: The symbol ∆ denotes one of the four arithmetic operations:addition,su
[#permalink]
09 Jan 2018, 17:39






